On the Frobenius Integrability of Certain Holomorphic p-Forms

Jean-Pierre Demailly ()
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Jean-Pierre Demailly: Université de Grenoble I, Département de Mathématiques, Institut Fourier

A chapter in Complex Geometry, 2002, pp 93-98 from Springer

Abstract: Abstract The goal of this note is to exhibit the integrability properties (in the sense of the Frobenius theorem) of holomorphic p-forms with values in certain line bundles with semi-negative curvature on a compact Kähler manifold. There are in fact very strong restrictions, both on the holomorphic form and on the curvature of the semi-negative line bundle. In particular, these observations provide interesting information on the structure of projective manifolds which admit a contact structure: either they are Fano manifolds or, thanks to results of Kebekus-Peternell-Sommese-Wisniewski, they are biholomorphic to the projectivization of the cotangent bundle of another suitable projective manifold.

Keywords: 2000; Mathematics Subject Classification; 32Q15; 32J25 (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-56202-0_6

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DOI: 10.1007/978-3-642-56202-0_6

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